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Dec16-12, 07:47 PM
Sci Advisor
P: 3,757
Quote Quote by nhmllr View Post
Okay, let's say my arm was perfectly efficient. Or let's say that the block is a magnet that we suspend on top of a perfectly efficient electro magnet that strengthens and weakens in it's field, causing the block to move up and down. Basically what I'm saying is, if there are no inefficiencies, where does the energy go?
If there were no inefficiencies, the the work you did lifting the block would be converted into an increase in gravitational potential energy. Then when the block came back down that potential energy would be converted into kinetic energy as the block accelerated under the influence of gravity, and it would be moving fairly quickly. Whatever is slowing the block so that it ends up at rest when gets back to ground level is dissipating that energy as heat.

Now, you could, with mythical perfectly efficient devices, arrange to rest the block on a mythical perfectly efficient spring. Then you could push the block down on the spring to compress it (doing work on and adding potential energy to the spring), and release the spring. The mythical perfectly efficient spring would accelerate the block upwards, converting all of the potential energy into kinetic energy of the moving block. The block would move upwards, slowing down and exchanging kinetic energy for gravitational potential energy, until its speed reached zero and it started to fall back down again, turning the potential energy back into kinetic energy... and in this mythical perfectly efficient world we wouldn't lose any energy to friction with the air, so the block would come down and compress the myhtical perfectly efficient spring with all the energy that we started with, and the cycle would repeat itself.

In this mythical perfectly efficient world you could keep the block moving up and down without ever losing any energy; no input beyond your initial shove would be needed. It's basically the same problem as an ideal pendulum in a mythical perfect vacuum hanging from a mythical perfectly frictionless hinge - give it a push and it will go forever in this mythical perfectly efficient world.

Did I mention that we're talking about a mythical world here?